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Chapter 6: Q 14. (page 369)

Skee Ball Ana is a dedicated Skee Ball player (see photo in Exercise 4) who always rolls for the 50-point slot. The probability distribution of Ana’s score X on a randomly selected roll of the ball is shown here. From Exercise 8, μX=23.8 . Calculate and interpret the standard deviation of X.

Short Answer

Expert verified

The standard deviation isσ=12.6317.

Step by step solution

01

Step 1. Given information.

The given information is:

02

Step 2. Find and interpret the standard deviation of X.

The given mean is 23.8.

The predicted value of the squared departure from the mean is known as the variance:

σ2=∑x-μ2Px=10-23.82×0.32+20-23.82×0.27+30-23.82×0.19+40-23.82×0.15+50-23.82×0.07=159.56

The standard deviation is:

σ=σ2=159.56≈12.6317

The average score on a randomly chosen roll of the ball is 12.6317 points higher than the mean score of 23.8.

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